4.2 Concept Check

• 18π

• 36π

• 9π

• 12π

Answer explanation

• 16

• 24

• 28

• 32

Answer explanation

• 15.5

• 13.25

• 12.15

• 11.5

• 15.75

• 16

• 16.5

• 15.25

Answer explanation

The integral represents the area under the graph on the interval [0, 8]. Use a combination of rectangles, triangles, and/or trapezoids to evaluate.

A note card company has found that the marginal cost per card of producing x note cards is given by the function below, where C'(x) is the marginal cost, in cents per card. Which of the following represents the total cost of producing 760 cards, assuming there are no fixed costs?

• C'(760)

• C'(760) - C'(0)

The graph shown represents the marginal profit (in cents per member) of a company with x members. Which of the following statements are true? Select all that apply.

• 
• 

Answer explanation

The definite integral of the marginal profit function represents the total amount of profit earned on the interval [0, 300]

AND can be approximated by using a Riemann Sum

AND that Approximation can be represented using Summation Notation.

A Riemann Sum uses rectangles to

• approximate the area under a curve. The more rectangles, the better the approximation.

• approximate the area under a curve. The fewer rectangles, the better the approximation.

• approximate the area under a curve. The more rectangles, the worse the approximation.

Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.) 

• 5(3) + 1(4) + 2(5) + 1(7)
• 5(4) + 1(5) + 2(7) + 1(6)
• 5(3) + 6(4) + 8(5) + 9(7)
• 0(3) + 5(4) + 6(5) + 8(7)

Answer explanation

In this table of values, the widths of each subinterval are not equal. The first rectangle is 5 units wide and f(0) units tall, etc.

Tags

CCSS.HSA.SSE.A.1